Frank Plumpton Ramsey (22 February 1903 – 19 January 1930) was a precocious British philosopher, mathematician and economist who died at the age of 26. He was a close friend of Ludwig Wittgenstein and was instrumental in translating Wittgenstein's Tractatus Logico-Philosophicus into English, as well as persuading Wittgenstein to return to philosophy and Cambridge. Like Wittgenstein, he was a member of the Cambridge Apostles, the intellectual secret society, from 1921.

Ramsey was born on 22 February 1903 in Cambridge where his father Arthur Stanley Ramsey (1867–1954), also a mathematician, was President of Magdalene College. His mother was Mary Agnes Stanley (1875–1927). He was the eldest of two brothers and two sisters, and his brother Michael Ramsey, the only one of the four siblings who was to remain Christian, later became Archbishop of Canterbury. He entered Winchester College in 1915 and later returned to Cambridge to study mathematics at Trinity College. While studying mathematics at Trinity College, Ramsey became a student to John Maynard Keynes, and an active member in the Apostles, a Cambridge discussion group. In 1923, he received his bachelor's degree in mathematics with high honours.[1] Easy-going, simple and modest, Ramsey had many interests besides his scientific work. Even as a teenager Ramsey exhibited both a profound ability and, as attested by his brother, an extremely diverse range of interests:

He was interested in almost everything. He was immensely widely read in English literature; he was enjoying classics though he was on the verge of plunging into being a mathematical specialist; he was very interested in politics, and well-informed; he had got a political concern and a sort of left-wing caring-for-the-underdog kind of outlook about politics.

— Michael Ramsey, Quoted in Mellor

In 1923, Ramsey was befriended by Geoffrey and Margaret Pyke, then on the point of founding the Malting House School in Cambridge; the Pykes took Ramsey into their family, taking him on holiday, asking him to be the godfather of their young son. Margaret Pyke found herself to be the object of his affection, Ramsey recording in his diary:

One afternoon I went out alone with her on Lake Orta and became filled with desire and we came back and lay on two beds side by side she reading, I pretending to, but with an awful conflict in my mind. After about an hour I said (she was wearing her horn spectacles and looking superlatively beautiful in the Burne Jones style) ‘Margaret will you fuck with me?’[2]

Margaret wanted time to consider his proposition and thus began an uncomfortable dance between them, which contributed to Ramsey's depressive moods in early 1924; as a result he travelled to Vienna for psychoanalysis. He, like many of his contemporaries, including his Viennese flatmate and fellow Apostle Lionel Penrose (also in analysis with Siegfried Bernfeld), was intellectually interested in psychoanalysis. Ramsey's analyst was Theodor Reik, a disciple of Freud. As one of the justifications for undertaking the therapy, he asserted in a letter to his mother that unconscious impulses might even affect the work of a mathematician. While in Vienna, he visited Wittgenstein in Puchberg, was befriended by the Wittgenstein family and visited A.S. Neill's experimental school four hours from Vienna at Sonntagsberg. In the summer of 1924, he continued his analysis by joining Reik at Dobbiaco(Sud-Tirol), where a fellow analysand was Lewis Namier. Ramsey returned to England in October 1924; with John Maynard Keynes's support he became a fellow of King's College, Cambridge. He joined a Psychoanalysis Group in Cambridge with fellow members Arthur Tansley, Lionel Penrose, Harold Jeffreys, John Rickman and James Strachey, the qualification for membership of which was a completed psychoanalysis.

Ramsey married Lettice Baker in September 1925, the wedding taking place in a Register Office since Ramsey was, as his wife described him, a ‘militant atheist'. (She subsequently ran a photography practice in Cambridge for many years ["Ramsey and Muspratt"].) The marriage produced two daughters. Despite his atheism, Ramsey was quite tolerant towards his brother when the latter decided to become a priest in the Church of England.[3]

In 1926 he became a university lecturer in mathematics and later a Director of Studies in Mathematics at King's College. The Vienna Circle manifesto (1929) lists three of his publications[4][5][6] in a bibliography of closely related authors.

When I. A. Richards and C. K. Ogden, both Fellows of Magdalene, first met Ramsey, he expressed his interest in learning German. According to Richards, he mastered the language "in almost hardly over a week",[7] although other sources show he took before that one year of German in school.[8] Ramsey was then able, at the age of 19, to make the first draft of the translation of the German text of Wittgenstein's Tractatus Logico Philosophicus. Ramsey was impressed by Wittgenstein's work and after graduating as Senior Wrangler in the Mathematical Tripos of 1923 he made a journey to Austria to visit Wittgenstein, at that time teaching in a primary school in the small community of Puchberg am Schneeberg. For two weeks Ramsey discussed the difficulties he was facing in understanding the Tractatus. Wittgenstein made some corrections to the English translation in Ramsey's copy and some annotations and changes to the German text that subsequently appeared in the second edition in 1933.

In 1929 Ramsey and Wittgenstein regularly discussed issues in mathematics and philosophy with Piero Sraffa, an Italian economist who had been brought to Cambridge by Keynes after Sraffa had aroused Benito Mussolini's ire by publishing an article critical of the Fascist regime in the Manchester Guardian. The contributions of Ramsey to these conversations were acknowledged by both Sraffa and Wittgenstein in their later work.

Ramsey’s notes and manuscripts were acquired by Nicholas Rescher for the Archives of Scientific Philosophy and the University of Pittsburgh. This Ramsey collection contains only a few letters but a great many drafts of papers and book chapters, some still unpublished. Other papers, including his Diary, some letters and Memoirs by his widow Lettice Ramsey and his father, are held in the Modern Archives, King's College, Cambridge.

One of the theorems proved by Ramsey in his 1928 paper On a problem of formal logic now bears his name (Ramsey's theorem). While this theorem is the work Ramsey is probably best remembered for, he only proved it in passing, as a minor lemma along the way to his true goal in the paper, solving a special case of the decision problem for first-order logic, namely the decidability of what is now called the Bernays–Schönfinkel–Ramsey class of first-order logic, as well as a characterisation of the spectrum of sentences in this fragment of logic. Alonzo Church would go on to show that the general case of the decision problem for first-order logic is unsolvable (see Church's theorem). A great amount of later work in mathematics was fruitfully developed out of the ostensibly minor lemma, which turned out to be an important early result in combinatorics, supporting the idea that within some sufficiently large systems, however disordered, there must be some order. So fruitful, in fact, was Ramsey's theorem that today there is an entire branch of mathematics, known as Ramsey theory, which is dedicated to studying similar results.

His philosophical works included Universals (1925), Facts and propositions (1927) (which proposed a redundancy theory of truth), Universals of law and of fact (1928), Knowledge (1929), Theories (1929), On Truth (1929), and General propositions and causality (1929). Wittgenstein mentions him in the introduction to his Philosophical Investigations as an influence.

Keynes and Pigou encouraged Ramsey to work on economics as "From a very early age, about sixteen I think, his precocious mind was intensely interested in economic problems" (Keynes, 1933). Ramsey responded to Keynes's urging by writing three papers in economic theory all of which were of fundamental importance, though it was many years before they received their proper recognition by the community of economists.

Ramsey's three papers, described below in detail, were on subjective probability and utility (1926), optimal taxation (1927) and optimal one-sector economic growth (1928). The economist Paul Samuelson described them in 1970 as "three great legacies – legacies that were for the most part mere by-products of his major interest in the foundations of mathematics and knowledge."[10]

Keynes described the article as "one of the most remarkable contributions to mathematical economics ever made, both in respect of the intrinsic importance and difficulty of its subject, the power and elegance of the technical methods employed, and the clear purity of illumination with which the writer's mind is felt by the reader to play about its subject. The article is terribly difficult reading for an economist, but it is not difficult to appreciate how scientific and aesthetic qualities are combined in it together" (Keynes 1933)[citation needed]. The Ramsey model is today acknowledged as the starting point for optimal accumulation theory although its importance was not recognised until many years after its first publication.

The main contributions of the model were firstly the initial question Ramsey posed on how much savings should be and secondly the method of analysis, the intertemporal maximisation (optimisation) of collective or individual utility by applying techniques of dynamic optimisation. Tjalling C. Koopmans and David Cass modified the Ramsey model incorporating the dynamic features of population growth at a steady rate and of Harrod-neutral technical progress again at a steady rate, giving birth to a model named the Ramsey–Cass–Koopmans model where the objective now is to maximise household's utility function.

In this paper Ramsey's contribution to economic theory was the elegant concept of Ramsey pricing. This is applicable in situations where a (regulated) monopolist wants to maximise consumer surplus whilst at the same time ensuring that its costs are adequately covered. This is achieved by setting the price such that the markup over marginal cost is inversely proportional to the price elasticity of demand for that good. Like its predecessor this paper was published in The Economic Journal in 1927. Ramsey poses the question that is to be solved at the beginning of the article: "a given revenue is to be raised by proportionate taxes on some or all uses of income, the taxes on different uses being possibly at different rates; how much should these rates be adjusted in order that the decrement of utility may be a minimum?" (Ramsey 1927). The problem was suggested to him by the economist Arthur Pigou and the paper was Ramsey's answer to the problem.

Keynes in his A Treatise on Probability (1921) argued against the subjective approach in epistemic probabilities. For Keynes, subjectivity of probabilities doesn't matter as much, as for him there is an objective relationship between knowledge and probabilities, as knowledge is disembodied and not personal.

Ramsey in his article disagrees with Keynes's approach as for him there is a difference between the notions of probability in physics and in logic. For Ramsey probability is not related to a disembodied body of knowledge but is related to the knowledge that each individual possesses alone. Thus personal beliefs that are formulated by this individual knowledge govern probabilities leading to the notion of subjective probability. Consequently, subjective probabilities can be inferred by observing actions that reflect individuals' personal beliefs. Ramsey argued that the degree of probability that an individual attaches to a particular outcome can be measured by finding what odds the individual would accept when betting on that outcome.

Ramsey suggested a way of deriving a consistent theory of choice under uncertainty that could isolate beliefs from preferences while still maintaining subjective probabilities.

Sahlin, N.-E. (1996), “He is no good for my work”: On the philosophical relations between Ramsey and Wittgenstein, in Knowledge and Inquiry: Essays on Jaakko Hintikkas Epistemology and Philosophy of Science, ed by M. Sintonen, Poznan Studies in the Philosophy of Sciences and the Humanities, Amsterdam, 61–84